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Diploma in AP Calculus AB

This free online course examines the properties and application of differentials, as well as principles of integration.

Publisher: ADU
This course introduces you to the basics of differential and integral calculus. It explains some of the most important concepts and theorems in calculus and, by the end, you will be able to solve real-world problems by applying the principles of differential and integral calculus. This material is equivalent to first semester college calculus and is suitable for those taking the AP (Advanced Placement) math exams.
Diploma in AP Calculus AB
  • Duration

    10-15 Hours
  • Students

  • Accreditation


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The study of limits and the closely related concept of continuity are essential for mastering calculus. While the concept of a limit is usually easy to grasp, calculating limits can be demanding if the functions do not conform to customary patterns. In this course, you will study the concept of the limit of a function and its application in different scenarios. Did you know that limits work hand in hand with continuity? This course defines the concepts and operations as they relate to limits and continuity. You will be introduced to the idea and concept of the limits of a function and how it is used to define the derivative of a function. In calculus, derivatives are used to measure the changes in a particular function. One of the important applications of calculus is in the analysis of the rate of change of events. The course discusses extensively the key ideas used in calculating the rate of change. You will study the behaviour of a function with limits. You will be taken through how to calculate the limits of functions using different methods.

We call the derivative of y' the second derivative of y and denote it by y" or f" (x). It is also essential to know that other higher-order derivatives, such as the third derivative, y'" can be applied in differential Calculus. One obtains y'" by differentiating y" in the same manner in which one differentiates y' to obtain y". In this course, you will learn how to calculate the derivatives of inverse trigonometric functions, including arcsine, arctangent and arcsecant. Do you know that the derivatives of trigonometric functions can also help you determine the derivatives for arccosine, arccotangent and arcsecant? You will be able to identify the restrictions that need to be placed on inverse derivatives for them to become functions. The arcsine is given to the inverse of sine. You will study how this function is written and the rationale behind the name. The course uses a basic method that will enable you to derive the formulas for the derivatives of the arc-cotangent and arc-cosecant functions. Another interesting concept discussed is logarithms. 

You will also be taken through the applications and properties of definite integrals. You will be introduced to the various methods used in estimating such as Riemann sums, sigma notation, and the properties of a definite integral. How important are the fundamental theorems of integral calculus? In this course, you will learn about the trapezoid approximation methods used in evaluating integrals. Learn about sigma notation, which is a convenient way to compress writing large sums during integration. An exciting part of sigma notation is that it can be used for sums involving subscripts. Another interesting concept is the three important laws of sigma notation. You will study how to get the exact area under a curve by using an approximation and subintervals and then taking the limit as a function approaches infinity. The course discusses in-depth some methods of integration, including integration by partial fractions. If you are a student looking to improve your knowledge of integral calculus and its amazing applications, then register for this course today. It is also very helpful for revising for the AP calculus exams.

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